During her short stint on court Griffin turned over the ball four times and connected with four of her five attempts at goal.
Her replacement Jamilah Gupwell didn't stamp her mark on the game either, shooting two from six, but was consistent in general play.
One of the major issues for the Pulse this year is their inability to feed the circle adequately and that continued today.
Ngarama Milner-Olsen began the game at wing attack but was pulled at half time as Camilla Lees pushed from centre in to the WA bib, replaced by Daya Wiffen.
Pulse coach Robyn Broughton wasn't happy with that mix for long though, inserting Katarina Cooper at wing attack for the final quarter and moving Lees back to centre.
Cooper's form was sound in the final stanza as she brought a different intensity to the attack. Lees was reliable in the middle of the court.
Australian import Caitlin Thwaites is one of the competition's leading shooters but she would have been disappointed to nail only 30 of her 37 attempts on goal.
Thwaites missed a pair of crucial shots in the fourth quarter as the Pulse mounted their comeback but failed to convert when her side needed it most.
Pulse captain Katrina Grant has been in fine touch throughout the opening five games of the season and is among the leaders in rebounds, deflections and intercepts.
Grant was at her best in the defensive circle and produced a phenomenal seven intercepts as she made life tough for the Swifts shooters.
Susan Pratley was composed for the home side as she shot 20 from 22.
The Pulse host the Magic in Porirua next week, and the Swifts host the Melbourne Vixens.
NSW Swifts 39 Central Pulse 36 HT: 24-15